Electron cryomicroscopy of biological machines at subnanometer resolution

Elastic Fibers in the Intervertebral Disc: From Form to Function and toward Regeneration

Despite extensive efforts over the past 40 years, there is still a significant gap in knowledge of the characteristics of elastic fibers in the intervertebral disc (IVD). More studies are required to clarify the potential contribution of elastic fibers to the IVD (healthy and diseased) function and recommend critical areas for future investigations. On the other hand, current IVD in-vitro models are not true reflections of the complex biological IVD tissue and the role of elastic fibers has often been ignored in developing relevant tissue-engineered scaffolds and realistic computational models. This has affected the progress of IVD studies (tissue engineering solutions, biomechanics, fundamental biology) and translation into clinical practice. Motivated by the current gap, the current review paper presents a comprehensive study (from the early 1980s to 2022) that explores the current understanding of structural (multi-scale hierarchy), biological (development and aging, elastin content, and cell-fiber interaction), and biomechanical properties of the IVD elastic fibers, and provides new insights into future investigations in this domain.

Cryo-ET of Toxoplasma parasites gives subnanometer insight into tubulin-based structures

Tubulin polymers are essential for a variety of cellular functions. Using cryo-ET, we reveal the 3D organization of the apical complex in Toxoplasma gondii, an intracellular eukaryote with tubulin-based structures, including an apical “conoid” involved in host cell invasion. Our development of an advanced subtomogram averaging protocol for filamentous structures enabled us to accurately assign tubulins in cellular context. At the subnanometer resolution achieved, tubulins were confirmed to assemble into two major forms: canonical subpellicular microtubules (SPMTs) and noncanonical conoid fibrils (CFs). The data further revealed associated proteins in both structures, a dominant orientation of SPMTs, and a unique patterning of the CFs. This work demonstrates an approach that can be used to determine cellular filamentous structures at multiscale resolutions.

Tubulin is a conserved protein that polymerizes into different forms of filamentous structures in Toxoplasma gondii, an obligate intracellular parasite in the phylum Apicomplexa. Two key tubulin-containing cytoskeletal components are subpellicular microtubules (SPMTs) and conoid fibrils (CFs). The SPMTs help maintain shape and gliding motility, while the CFs are implicated in invasion. Here, we use cryogenic electron tomography to determine the molecular structures of the SPMTs and CFs in vitrified intact and detergent-extracted parasites. Subvolume densities from detergent-extracted parasites yielded averaged density maps at subnanometer resolutions, and these were related back to their architecture in situ. An intralumenal spiral lines the interior of the 13-protofilament SPMTs, revealing a preferred orientation of these microtubules relative to the parasite’s long axis. Each CF is composed of nine tubulin protofilaments that display a comma-shaped cross-section, plus additional associated components. Conoid protrusion, a crucial step in invasion, is associated with an altered pitch of each CF. The use of basic building blocks of protofilaments and different accessory proteins in one organism illustrates the versatility of tubulin to form two distinct types of assemblies, SPMTs and CFs.

The allosteric control mechanism of bacterial glycogen biosynthesis disclosed by cryoEM

Glycogen and starch are the major carbon and energy reserve polysaccharides in nature, providing living organisms with a survival advantage. The evolution of the enzymatic machinery responsible for the biosynthesis and degradation of such polysaccharides, led the development of mechanisms to control the assembly and disassembly rate, to store and recover glucose according to cell energy demands. The tetrameric enzyme ADP-glucose pyrophosphorylase (AGPase) catalyzes and regulates the initial step in the biosynthesis of both α-polyglucans. AGPase displays cooperativity and allosteric regulation by sensing metabolites from the cell energy flux. The understanding of the allosteric signal transduction mechanisms in AGPase arises as a long-standing challenge. In this work, we disclose the cryoEM structures of the paradigmatic homotetrameric AGPase from Escherichia coli (EcAGPase), in complex with either positive or negative physiological allosteric regulators, fructose-1,6-bisphosphate (FBP) and AMP respectively, both at 3.0 Å resolution. Strikingly, the structures reveal that FBP binds deeply into the allosteric cleft and overlaps the AMP site. As a consequence, FBP promotes a concerted conformational switch of a regulatory loop, RL2, from a "locked" to a "free" state, modulating ATP binding and activating the enzyme. This notion is strongly supported by our complementary biophysical and bioinformatics evidence, and a careful analysis of vast enzyme kinetics data on single-point mutants of EcAGPase. The cryoEM structures uncover the residue interaction networks (RIN) between the allosteric and the catalytic components of the enzyme, providing unique details on how the signaling information is transmitted across the tetramer, from which cooperativity emerges. Altogether, the conformational states visualized by cryoEM reveal the regulatory mechanism of EcAGPase, laying the foundations to understand the allosteric control of bacterial glycogen biosynthesis at the molecular level of detail.

Evolving data standards for cryo-EM structures

Electron cryo-microscopy (cryo-EM) is increasingly being used to determine 3D structures of a broad spectrum of biological specimens from molecules to cells. Anticipating this progress in the early 2000s, an international collaboration of scientists with expertise in both cryo-EM and structure data archiving was established (EMDataResource, previously known as EMDataBank). The major goals of the collaboration have been twofold: to develop the necessary infrastructure for archiving cryo-EM-derived density maps and models, and to promote development of cryo-EM structure validation standards. We describe how cryo-EM data archiving and validation have been developed and jointly coordinated for the Electron Microscopy Data Bank and Protein Data Bank archives over the past two decades, as well as the impact of evolving technology on data standards. Just as for X-ray crystallography and nuclear magnetic resonance, engaging the scientific community via workshops and challenging activities has played a central role in developing recommendations and requirements for the cryo-EM structure data archives.

Archiving and disseminating integrative structure models

Limitations in the applicability, accuracy, and precision of individual structure characterization methods can sometimes be overcome via an integrative modeling approach that relies on information from all available sources, including all available experimental data and prior models. The open-source Integrative Modeling Platform (IMP) is one piece of software that implements all computational aspects of integrative modeling. To maximize the impact of integrative structures, the coordinates should be made publicly available, as is already the case for structures based on X-ray crystallography, NMR spectroscopy, and electron microscopy. Moreover, the associated experimental data and modeling protocols should also be archived, such that the original results can easily be reproduced. Finally, it is essential that the integrative structures are validated as part of their publication and deposition. A number of research groups have already developed software to implement integrative modeling and have generated a number of structures, prompting the formation of an Integrative/Hybrid Methods Task Force. Following the recommendations of this task force, the existing PDBx/mmCIF data representation used for atomic PDB structures has been extended to address the requirements for archiving integrative structural models. This IHM-dictionary adds a flexible model representation, including coarse graining, models in multiple states and/or related by time or other order, and multiple input experimental information sources. A prototype archiving system called PDB-Dev ( https://pdb-dev.wwpdb.org ) has also been created to archive integrative structural models, together with a Python library to facilitate handling of integrative models in PDBx/mmCIF format.

Modeling Biological Complexes Using Integrative Modeling Platform

Integrative structure modeling provides 3D models of macromolecular systems that are based on information from multiple types of experiments, physical principles, statistical inferences, and prior structural models. Here, we provide a hands-on realistic example of integrative structure modeling of the quaternary structure of the actin, tropomyosin, and gelsolin protein assembly based on electron microscopy, solution X-ray scattering, and chemical crosslinking data for the complex as well as excluded volume, sequence connectivity, and rigid atomic X-ray structures of the individual subunits. We follow the general four-stage process for integrative modeling, including gathering the input information, converting the input information into a representation of the system and a scoring function, sampling alternative model configurations guided by the scoring function, and analyzing the results. The computational aspects of this approach are implemented in our open-source Integrative Modeling Platform (IMP), a comprehensive and extensible software package for integrative modeling ( https://integrativemodeling.org ). In particular, we rely on the Python Modeling Interface (PMI) module of IMP that provides facile mixing and matching of macromolecular representations, restraints based on different types of information, sampling algorithms, and analysis including validations of the input data and output models. Finally, we also outline how to deposit an integrative structure and corresponding experimental data into PDB-Dev, the nascent worldwide Protein Data Bank (wwPDB) resource for archiving and disseminating integrative structures ( https://pdb-dev.wwpdb.org ). The example application provides a starting point for a user interested in using IMP for integrative modeling of other biomolecular systems.

Lipid bilayer-atomic force microscopy combined platform records simultaneous electrical and topological changes of the TRP channel polycystin-2 (TRPP2)

Ion channels are transmembrane proteins that mediate ion transport across biological membranes. Ion channel function is traditionally characterized by electrical parameters acquired with techniques such as patch-clamping and reconstitution in lipid bilayer membranes (BLM) that provide relevant information such as ionic conductance, selectivity, and gating properties. High resolution structural information of ion channels however, requires independent technologies, of which atomic force microscopy (AFM) is the only one that provides topological features of single functional channel proteins in their native environments. To date practically no data exist on direct correlations between electrical features and topological parameters from functional single channel complexes. Here, we report the design and construction of a BLM reconstitution microchamber that supports the simultaneous recording of electrical currents and AFM imaging from single channel complexes. As proof-of-principle, we tested the technique on polycystin-2 (PC2, TRPP2), a TRP channel family member from which we had previously elucidated its tetrameric topology by AFM imaging, and single channel currents by the BLM technique. The experimental setup provided direct structural-functional correlates from PC2 single channel complexes that disclosed novel topological changes between the closed and open sub-conductance states of the functional channel, namely, an inverse correlation between conductance and height of the channel. Unexpectedly, we also disclosed intrinsic PC2 mechanosensitivity in response to external forces. The platform provides a suitable means of accessing topological information to correlate with ion channel electrical parameters essential to understand the physiology of these transmembrane proteins.

Anticipating innovations in structural biology

In this review, we describe how the interplay among science, technology and community interests contributed to the evolution of four structural biology data resources. We present the method by which data deposited by scientists are prepared for worldwide distribution, and argue that data archiving in a trusted repository must be an integral part of any scientific investigation.

Normal mode-guided transition pathway generation in proteins

The biological function of proteins is closely related to its structural motion. For instance, structurally misfolded proteins do not function properly. Although we are able to experimentally obtain structural information on proteins, it is still challenging to capture their dynamics, such as transition processes. Therefore, we need a simulation method to predict the transition pathways of a protein in order to understand and study large functional deformations. Here, we present a new simulation method called normal mode-guided elastic network interpolation (NGENI) that performs normal modes analysis iteratively to predict transition pathways of proteins. To be more specific, NGENI obtains displacement vectors that determine intermediate structures by interpolating the distance between two end-point conformations, similar to a morphing method called elastic network interpolation. However, the displacement vector is regarded as a linear combination of the normal mode vectors of each intermediate structure, in order to enhance the physical sense of the proposed pathways. As a result, we can generate more reasonable transition pathways geometrically and thermodynamically. By using not only all normal modes, but also in part using only the lowest normal modes, NGENI can still generate reasonable pathways for large deformations in proteins. This study shows that global protein transitions are dominated by collective motion, which means that a few lowest normal modes play an important role in this process. NGENI has considerable merit in terms of computational cost because it is possible to generate transition pathways by partial degrees of freedom, while conventional methods are not capable of this.

Integrative structure modeling with the Integrative Modeling Platform

Building models of a biological system that are consistent with the myriad data available is one of the key challenges in biology. Modeling the structure and dynamics of macromolecular assemblies, for example, can give insights into how biological systems work, evolved, might be controlled, and even designed. Integrative structure modeling casts the building of structural models as a computational optimization problem, for which information about the assembly is encoded into a scoring function that evaluates candidate models. Here, we describe our open source software suite for integrative structure modeling, Integrative Modeling Platform (https://integrativemodeling.org), and demonstrate its use.

Cryo-EM reconstruction of the Cafeteria roenbergensis virus capsid suggests novel assembly pathway for giant viruses

Whereas the protein composition and overall shape of several giant virus capsids have been described, the mechanism by which these large capsids assemble remains enigmatic. Here, we present a reconstruction of the capsid of Cafeteria roenbergensis virus (CroV), one of the largest viruses analyzed by cryo-electron microscopy (cryo-EM) to date. The CroV capsid has a diameter of 3,000 Å and a Triangulation number of 499. Unlike related mimiviruses, the CroV capsid is not decorated with glycosylated surface fibers, but features 30 Å-long surface protrusions that are formed by loops of the major capsid protein. Based on the orientation of capsomers in the cryo-EM reconstruction, we propose that the capsids of CroV and related giant viruses are assembled by a newly conceived assembly pathway that initiates at a five-fold vertex and continuously proceeds outwards in a spiraling fashion.

An Effective Computational Method Incorporating Multiple Secondary Structure Predictions in Topology Determination for Cryo-EM Images

A key idea in de novo modeling of a medium-resolution density image obtained from cryo-electron microscopy is to compute the optimal mapping between the secondary structure traces observed in the density image and those predicted on the protein sequence. When secondary structures are not determined precisely, either from the image or from the amino acid sequence of the protein, the computational problem becomes more complex. We present an efficient method that addresses the secondary structure placement problem in presence of multiple secondary structure predictions and computes the optimal mapping. We tested the method using 12 simulated images from α-proteins and two Cryo-EM images of α-β proteins. We observed that the rank of the true topologies is consistently improved by using multiple secondary structure predictions instead of a single prediction. The results show that the algorithm is robust and works well even when errors/misses in the predicted secondary structures are present in the image or the sequence. The results also show that the algorithm is efficient and is able to handle proteins with as many as 33 helices.

Bayesian Modeling of Biomolecular Assemblies with Cryo-EM Maps

A growing array of experimental techniques allows us to characterize the three-dimensional structure of large biological assemblies at increasingly higher resolution. In addition to X-ray crystallography and nuclear magnetic resonance in solution, new structure determination methods such cryo-electron microscopy (cryo-EM), crosslinking/mass spectrometry and solid-state NMR have emerged. Often it is not sufficient to use a single experimental method, but complementary data need to be collected by using multiple techniques. The integration of all datasets can only be achieved by computational means. This article describes Inferential structure determination, a Bayesian approach to integrative modeling of biomolecular complexes with hybrid structural data. I will introduce probabilistic models for cryo-EM maps and outline Markov chain Monte Carlo algorithms for sampling model structures from the posterior distribution. I will focus on rigid and flexible modeling with cryo-EM data and discuss some of the computational challenges of Bayesian inference in the context of biomolecular modeling.

Modeling Beta-Traces for Beta-Barrels from Cryo-EM Density Maps

Cryo-electron microscopy (cryo-EM) has produced density maps of various resolutions. Although α-helices can be detected from density maps at 5-8 Å resolutions, β-strands are challenging to detect at such density maps due to close-spacing of β-strands. The variety of shapes of β-sheets adds the complexity of β-strands detection from density maps. We propose a new approach to model traces of β-strands for β-barrel density regions that are extracted from cryo-EM density maps. In the test containing eight β-barrels extracted from experimental cryo-EM density maps at 5.5 Å-8.25 Å resolution, StrandRoller detected about 74.26% of the amino acids in the β-strands with an overall 2.05 Å 2-way distance between the detected β-traces and the observed ones, if the best of the fifteen detection cases is considered.

Structural and mechanistic insights into human splicing factor SF3b complex derived using an integrated approach guided by the cryo-EM density maps

Pre-mRNA splicing in eukaryotes is performed by the spliceosome, a highly complex macromolecular machine. SF3b is a multi-protein complex which recognizes the branch point adenosine of pre-mRNA as part of a larger U2 snRNP or U11/U12 di-snRNP in the dynamic spliceosome machinery. Although a cryo-EM map is available for human SF3b complex, the structure and relative spatial arrangement of all components in the complex are not yet known. We have recognized folds of domains in various proteins in the assembly and generated comparative models. Using an integrative approach involving structural and other experimental data, guided by the available cryo-EM density map, we deciphered a pseudo-atomic model of the closed form of SF3b which is found to be a "fuzzy complex" with highly flexible components and multiplicity of folds. Further, the model provides structural information for 5 proteins (SF3b10, SF3b155, SF3b145, SF3b130 and SF3b14b) and localization information for 4 proteins (SF3b10, SF3b145, SF3b130 and SF3b14b) in the assembly for the first time. Integration of this model with the available U11/U12 di-snRNP cryo-EM map enabled elucidation of an open form. This now provides new insights on the mechanistic features involved in the transition between closed and open forms pivoted by a hinge region in the SF3b155 protein that also harbors cancer causing mutations. Moreover, the open form guided model of the 5' end of U12 snRNA, which includes the branch point duplex, shows that the architecture of SF3b acts as a scaffold for U12 snRNA: pre-mRNA branch point duplex formation with potential implications for branch point adenosine recognition fidelity.

Use of evolutionary information in the fitting of atomic level protein models in low resolution cryo-EM map of a protein assembly improves the accuracy of the fitting

Protein-protein interface residues, especially those at the core of the interface, exhibit higher conservation than residues in solvent exposed regions. Here, we explore the ability of this differential conservation to evaluate fittings of atomic models in low-resolution cryo-EM maps and select models from the ensemble of solutions that are often proposed by different model fitting techniques. As a prelude, using a non-redundant and high-resolution structural dataset involving 125 permanent and 95 transient complexes, we confirm that core interface residues are conserved significantly better than nearby non-interface residues and this result is used in the cryo-EM map analysis. From the analysis of inter-component interfaces in a set of fitted models associated with low-resolution cryo-EM maps of ribosomes, chaperones and proteasomes we note that a few poorly conserved residues occur at interfaces. Interestingly a few conserved residues are not in the interface, though they are close to the interface. These observations raise the potential requirement of refitting the models in the cryo-EM maps. We show that sampling an ensemble of models and selection of models with high residue conservation at the interface and in good agreement with the density helps in improving the accuracy of the fit. This study indicates that evolutionary information can serve as an additional input to improve and validate fitting of atomic models in cryo-EM density maps.

De Novo modeling in cryo-EM density maps with Pathwalking

As electron cryo-microscopy (cryo-EM) can now frequently achieve near atomic resolution, accurate interpretation of these density maps in terms of atomistic detail has become paramount in deciphering macromolecular structure and function. However, there are few software tools for modeling protein structure from cryo-EM density maps in this resolution range. Here, we present an extension of our original Pathwalking protocol, which can automatically trace a protein backbone directly from a near-atomic resolution (3-6Å) density map. The original Pathwalking approach utilized a Traveling Salesman Problem solver for backbone tracing, but manual adjustment was still required during modeling. In the new version, human intervention is minimized and we provide a more robust approach for backbone modeling. This includes iterative secondary structure identification, termini detection and the ability to model multiple subunits without prior segmentation. Overall, the new Pathwalking procedure provides a more complete and robust tool for annotating protein structure function in near-atomic resolution density maps.

High-resolution modeling of protein structures based on flexible fitting of low-resolution structural data

To circumvent the difficulty of directly solving high-resolution biomolecular structures, low-resolution structural data from Cryo-electron microscopy (EM) and small angle solution X-ray scattering (SAXS) are increasingly used to explore multiple conformational states of biomolecular assemblies. One promising venue to obtain high-resolution structural models from low-resolution data is via data-constrained flexible fitting. To this end, we have developed a new method based on a coarse-grained Cα-only protein representation, and a modified form of the elastic network model (ENM) that allows large-scale conformational changes while maintaining the integrity of local structures including pseudo-bonds and secondary structures. Our method minimizes a pseudo-energy which linearly combines various terms of the modified ENM energy with an EM/SAXS-fitting score and a collision energy that penalizes steric collisions. Unlike some previous flexible fitting efforts using the lowest few normal modes, our method effectively utilizes all normal modes so that both global and local structural changes can be fully modeled with accuracy. This method is also highly efficient in computing time. We have demonstrated our method using adenylate kinase as a test case which undergoes a large open-to-close conformational change. The EM-fitting method is available at a web server (http://enm.lobos.nih.gov), and the SAXS-fitting method is available as a pre-compiled executable upon request.

Imaging live cells at the nanometer-scale with single-molecule microscopy: obstacles and achievements in experiment optimization for microbiology

Single-molecule fluorescence microscopy enables biological investigations inside living cells to achieve millisecond- and nanometer-scale resolution. Although single-molecule-based methods are becoming increasingly accessible to non-experts, optimizing new single-molecule experiments can be challenging, in particular when super-resolution imaging and tracking are applied to live cells. In this review, we summarize common obstacles to live-cell single-molecule microscopy and describe the methods we have developed and applied to overcome these challenges in live bacteria. We examine the choice of fluorophore and labeling scheme, approaches to achieving single-molecule levels of fluorescence, considerations for maintaining cell viability, and strategies for detecting single-molecule signals in the presence of noise and sample drift. We also discuss methods for analyzing single-molecule trajectories and the challenges presented by the finite size of a bacterial cell and the curvature of the bacterial membrane.

Protruding knob-like proteins violate local symmetries in an icosahedral marine virus

Marine viruses play crucial roles in shaping the dynamics of oceanic microbial communities and in the carbon cycle on Earth. Here we report a 4.7-Å structure of a cyanobacterial virus, Syn5, by electron cryo-microscopy and modelling. A Cα backbone trace of the major capsid protein (gp39) reveals a classic phage protein fold. In addition, two knob-like proteins protruding from the capsid surface are also observed. Using bioinformatics and structure analysis tools, these proteins are identified to correspond to gp55 and gp58 (each with two copies per asymmetric unit). The non 1:1 stoichiometric distribution of gp55/58 to gp39 breaks all expected local symmetries and leads to non-quasi-equivalence of the capsid subunits, suggesting a role in capsid stabilization. Such a structural arrangement has not yet been observed in any known virus structures.

Single particle cryo-electron microscopy and 3-D reconstruction of viruses

With fast progresses in instrumentation, image processing algorithms, and computational resources, single particle electron cryo-microscopy (cryo-EM) 3-D reconstruction of icosahedral viruses has now reached near-atomic resolutions (3-4 Å). With comparable resolutions and more predictable outcomes, cryo-EM is now considered a preferred method over X-ray crystallography for determination of atomic structure of icosahedral viruses. At near-atomic resolutions, all-atom models or backbone models can be reliably built that allow residue level understanding of viral assembly and conformational changes among different stages of viral life cycle. With the developments of asymmetric reconstruction, it is now possible to visualize the complete structure of a complex virus with not only its icosahedral shell but also its multiple non-icosahedral structural features. In this chapter, we will describe single particle cryo-EM experimental and computational procedures for both near-atomic resolution reconstruction of icosahedral viruses and asymmetric reconstruction of viruses with both icosahedral and non-icosahedral structure components. Procedures for rigorous validation of the reconstructions and resolution evaluations using truly independent de novo initial models and refinements are also introduced.

Combining image processing and modeling to generate traces of beta-strands from cryo-EM density images of beta-barrels

Electron cryo-microscopy (Cryo-EM) technique produces 3-dimensional (3D) density images of proteins. When resolution of the images is not high enough to resolve the molecular details, it is challenging for image processing methods to enhance the molecular features. β-barrel is a particular structure feature that is formed by multiple β-strands in a barrel shape. There is no existing method to derive β-strands from the 3D image of a β-barrel at medium resolutions. We propose a new method, StrandRoller, to generate a small set of possible β-traces from the density images at medium resolutions of 5-10Å. StrandRoller has been tested using eleven β-barrel images simulated to 10Å resolution and one image isolated from the experimentally derived cryo-EM density image at 6.7Å resolution. StrandRoller was able to detect 81.84% of the β-strands with an overall 1.5Å 2-way distance between the detected and the observed β-traces, if the best of fifteen detections is considered. Our results suggest that it is possible to derive a small set of possible β-traces from the β-barrel cryo-EM image at medium resolutions even when no separation of the β-strands is visible in the images.

Modeling of proteins and their assemblies with the Integrative Modeling Platform

To understand the workings of the living cell, we need to characterize protein assemblies that constitute the cell (for example, the ribosome, 26S proteasome, and the nuclear pore complex). A reliable high-resolution structural characterization of these assemblies is frequently beyond the reach of current experimental methods, such as X-ray crystallography, NMR spectroscopy, electron microscopy, footprinting, chemical cross-linking, FRET spectroscopy, small angle X-ray scattering, and proteomics. However, the information garnered from different methods can be combined and used to build models of the assembly structures that are consistent with all of the available datasets, and therefore more accurate, precise, and complete. Here, we describe a protocol for this integration, whereby the information is converted to a set of spatial restraints and a variety of optimization procedures can be used to generate models that satisfy the restraints as well as possible. These generated models can then potentially inform about the precision and accuracy of structure determination, the accuracy of the input datasets, and further data generation. We also demonstrate the Integrative Modeling Platform (IMP) software, which provides the necessary computational framework to implement this protocol, and several applications for specific use cases.

Cryo-EM model validation using independent map reconstructions

An increasing number of cryo-electron microscopy (cryo-EM) density maps are being generated with suitable resolution to trace the protein backbone and guide sidechain placement. Generating and evaluating atomic models based on such maps would be greatly facilitated by independent validation metrics for assessing the fit of the models to the data. We describe such a metric based on the fit of atomic models with independent test maps from single particle reconstructions not used in model refinement. The metric provides a means to determine the proper balance between the fit to the density and model energy and stereochemistry during refinement, and is likely to be useful in determining values of model building and refinement metaparameters quite generally.

Bayesian analysis of individual electron microscopy images: towards structures of dynamic and heterogeneous biomolecular assemblies

We develop a method to extract structural information from electron microscopy (EM) images of dynamic and heterogeneous molecular assemblies. To overcome the challenge of disorder in the imaged structures, we analyze each image individually, avoiding information loss through clustering or averaging. The Bayesian inference of EM (BioEM) method uses a likelihood-based probabilistic measure to quantify the consistency between each EM image and given structural models. The likelihood function accounts for uncertainties in the molecular position and orientation, variations in the relative intensities and noise in the experimental images. The BioEM formalism is physically intuitive and mathematically simple. We show that for experimental GroEL images, BioEM correctly identifies structures according to the functional state. The top-ranked structure is the corresponding X-ray crystal structure, followed by an EM structure generated previously from a superset of the EM images used here. To analyze EM images of highly flexible molecules, we propose an ensemble refinement procedure, and validate it with synthetic EM maps of the ESCRT-I-II supercomplex. Both the size of the ensemble and its structural members are identified correctly. BioEM offers an alternative to 3D-reconstruction methods, extracting accurate population distributions for highly flexible structures and their assemblies. We discuss limitations of the method, and possible applications beyond ensemble refinement, including the cross-validation and unbiased post-assessment of model structures, and the structural characterization of systems where traditional approaches fail. Overall, our results suggest that the BioEM framework can be used to analyze EM images of both ordered and disordered molecular systems.

Computational methods for constructing protein structure models from 3D electron microscopy maps

Protein structure determination by cryo-electron microscopy (EM) has made significant progress in the past decades. Resolutions of EM maps have been improving as evidenced by recently reported structures that are solved at high resolutions close to 3Å. Computational methods play a key role in interpreting EM data. Among many computational procedures applied to an EM map to obtain protein structure information, in this article we focus on reviewing computational methods that model protein three-dimensional (3D) structures from a 3D EM density map that is constructed from two-dimensional (2D) maps. The computational methods we discuss range from de novo methods, which identify structural elements in an EM map, to structure fitting methods, where known high resolution structures are fit into a low-resolution EM map. A list of available computational tools is also provided.

Cellular nanoimaging by cryo electron tomography

Cryo electron tomography is a technique that allows visualization of biological specimens in three dimensions with nanometer resolution. For cryo immobilized life sciences samples it can reveal cellular morphology, the shape of membranous structures, and depict internal macromolecular arrangements and large proteins. Cryo electron tomography is a unique technique in structural biology research because it is the only tool that enables direct visualization of the cellular space at molecular resolution. Here we present the methods that we apply in our lab to perform cellular cryo electron tomography, which require expertise on cell biology for cell growth, physics for electron microscopy, and image processing for reconstruction and 3D visualization. We define the instrumentation, materials, and protocols for cryo electron tomography of whole cells, including cell growth, specimen vitrification, microscope alignments, data acquisition, tomographic image reconstruction, and 3D visualization techniques.

Nhs: network-based hierarchical segmentation for cryo-electron microscopy density maps

Cryo-electron microscopy (cryo-EM) experiments yield low-resolution (3-30 Å) 3D-density maps of macromolecules. These density maps are segmented to identify structurally distinct proteins, protein domains, and subunits. Such partitioning aids the inference of protein motions and guides fitting of high-resolution atomistic structures. Cryo-EM density map segmentation has traditionally required tedious and subjective manual partitioning or semisupervised computational methods, whereas validation of resulting segmentations has remained an open problem in this field. We introduce a network-based hierarchical segmentation (Nhs) method, that provides a multi-scale partitioning, reflecting local and global clustering, while requiring no user input. This approach models each map as a graph, where map voxels constitute nodes and weighted edges connect neighboring voxels. Nhs initiates Markov diffusion (or random walk) on the weighted graph. As Markov probabilities homogenize through diffusion, an intrinsic segmentation emerges. We validate the segmentations with ground-truth maps based on atomistic models. When implemented on density maps in the 2010 Cryo-EM Modeling Challenge, Nhs efficiently and objectively partitions macromolecules into structurally and functionally relevant subregions at multiple scales.

Macromolecular structure modeling from 3D EM using VolRover 2.0

We review tools for structure identification and model-based refinement from three-dimensional electron microscopy implemented in our in-house software package, VOLROVER 2.0. For viral density maps with icosahedral symmetry, we segment the capsid, polymeric, and monomeric subunits using techniques based on automatic symmetry detection and multidomain fast marching. For large biomolecules without symmetry information, we again use our multidomain fast-marching method with manual or fit-based multiseeding to segment meaningful substructures. In either case, we subject the resulting segmented subunit to secondary structure detection when the EM resolution is sufficiently high, and rigid-body structure fitting when the corresponding X-ray structure is available. Secondary structure elements are identified by three techniques: our earlier volume-based and boundary-based skeletonization methods as well as a new method, currently in development, based on solving the grassfire flow equation. For rigid-body fitting, we adapt our earlier fast Fourier-based correlation scheme F2Dock. Our reported segmentation, secondary structure elements identification, and rigid-body fitting techniques, implemented in VOLROVER 2.0 are applied to the PSB 2011 cryo-EM modeling challenge data, and our results are briefly compared to similar results submitted from other research groups. The comparisons show that our techniques are equally capable of segmenting relatively accurate subunits from a viral or protein assembly, and that high segmentation quality leads in turn to higher-quality results of secondary structure elements identification and correlation-based rigid-body fitting. © 2012 Wiley Periodicals, Inc. Biopolymers 97: 709-731, 2012.

Near-atomic-resolution cryo-EM for molecular virology

Electron cryo-microscopy (cryo-EM) is a technique in structural biology that is widely used to solve the three-dimensional structures of macromolecular assemblies, close to their biological and solution conditions. Recent improvements in cryo-EM and single-particle reconstruction methodologies have led to the determination of several virus structures at near-atomic resolution (3.3 - 4.6 Å). These cryo-EM structures not only resolve the Cα backbones and side-chain densities of viral capsid proteins, but also suggest functional roles that the protein domains and some key amino acid residues play. This paper reviews the recent advances in near-atomic-resolution cryo-EM for probing the mechanisms of virus assembly and morphogenesis.

Reconstructing virus structures from nanometer to near-atomic resolutions with cryo-electron microscopy and tomography

The past few decades have seen tremendous advances in single-particle electron -cryo-microscopy (cryo-EM). The field has matured to the point that near-atomic resolution density maps can be generated for icosahedral viruses without the need for crystallization. In parallel, substantial progress has been made in determining the structures of nonicosahedrally arranged proteins in viruses by employing either single-particle cryo-EM or cryo-electron tomography (cryo-ET). Implicit in this course have been the availability of a new generation of electron cryo-microscopes and the development of the computational tools that are essential for generating these maps and models. This methodology has enabled structural biologists to analyze structures in increasing detail for virus particles that are in different morphogenetic states. Furthermore, electron imaging of frozen, hydrated cells, in the process of being infected by viruses, has also opened up a new avenue for studying virus structures "in situ". Here we present the common techniques used to acquire and process cryo-EM and cryo-ET data and discuss their implications for structural virology both now and in the future.

Macromolecular assembly structures by comparative modeling and electron microscopy

Advances in electron microscopy allow for structure determination of large biological machines at increasingly higher resolutions. A key step in this process is fitting component structures into the electron microscopy-derived density map of their assembly. Comparative modeling can contribute by providing atomic models of the components, via fold assignment, sequence-structure alignment, model building, and model assessment. All four stages of comparative modeling can also benefit from consideration of the density map. In this chapter, we describe numerous types of modeling problems restrained by a density map and available protocols for finding solutions. In particular, we provide detailed instructions for density map-guided modeling using the Integrative Modeling Platform (IMP), MODELLER, and UCSF Chimera.

DERIVING TOPOLOGY AND SEQUENCE ALIGNMENT FOR THE HELIX SKELETON IN LOW-RESOLUTION PROTEIN DENSITY MAPS

Cryoelectron microscopy (cryoEM) is an experimental technique to determine the three-dimensional (3D) structure of large protein complexes. Currently, this technique is able to generate protein density maps at 6–9 Å resolution, at which the skeleton of the structure (which is composed of α-helices and β-sheets) can be visualized. As a step towards predicting the entire backbone of the protein from the protein density map, we developed a method to predict the topology and sequence alignment for the skeleton helices. Our method combines the geometrical information of the skeleton helices with the Rosetta ab initio structure prediction method to derive a consensus topology and sequence alignment for the skeleton helices. We tested the method with 60 proteins. For 45 proteins, the majority of the skeleton helices were assigned a correct topology from one of our top ten predictions. The offsets of the alignment for most of the assigned helices were within ±2 amino acids in the sequence. We also analyzed the use of the skeleton helices as a clustering tool for the decoy structures generated by Rosetta. Our comparison suggests that the topology clustering is a better method than a general overlap clustering method to enrich the ranking of decoys, particularly when the decoy pool is small.

Three-Dimensional Structure Determination from Common Lines in Cryo-EM by Eigenvectors and Semidefinite Programming()

The cryo-electron microscopy reconstruction problem is to find the three-dimensional (3D) structure of a macromolecule given noisy samples of its two-dimensional projection images at unknown random directions. Present algorithms for finding an initial 3D structure model are based on the "angular reconstitution" method in which a coordinate system is established from three projections, and the orientation of the particle giving rise to each image is deduced from common lines among the images. However, a reliable detection of common lines is difficult due to the low signal-to-noise ratio of the images. In this paper we describe two algorithms for finding the unknown imaging directions of all projections by minimizing global self-consistency errors. In the first algorithm, the minimizer is obtained by computing the three largest eigenvectors of a specially designed symmetric matrix derived from the common lines, while the second algorithm is based on semidefinite programming (SDP). Compared with existing algorithms, the advantages of our algorithms are five-fold: first, they accurately estimate all orientations at very low common-line detection rates; second, they are extremely fast, as they involve only the computation of a few top eigenvectors or a sparse SDP; third, they are nonsequential and use the information in all common lines at once; fourth, they are amenable to a rigorous mathematical analysis using spectral analysis and random matrix theory; and finally, the algorithms are optimal in the sense that they reach the information theoretic Shannon bound up to a constant for an idealized probabilistic model.

Exploring the spatial and temporal organization of a cell's proteome

To increase our current understanding of cellular processes, such as cell signaling and division, knowledge is needed about the spatial and temporal organization of the proteome at different organizational levels. These levels cover a wide range of length and time scales: from the atomic structures of macromolecules for inferring their molecular function, to the quantitative description of their abundance, and spatial distribution in the cell. Emerging new experimental technologies are greatly increasing the availability of such spatial information on the molecular organization in living cells. This review addresses three fields that have significantly contributed to our understanding of the proteome's spatial and temporal organization: first, methods for the structure determination of individual macromolecular assemblies, specifically the fitting of atomic structures into density maps generated from electron microscopy techniques; second, research that visualizes the spatial distributions of these complexes within the cellular context using cryo electron tomography techniques combined with computational image processing; and third, methods for the spatial modeling of the dynamic organization of the proteome, specifically those methods for simulating reaction and diffusion of proteins and complexes in crowded intracellular fluids. The long-term goal is to integrate the varied data about a proteome's organization into a spatially explicit, predictive model of cellular processes.

Determining macromolecular assembly structures by molecular docking and fitting into an electron density map

Structural models of macromolecular assemblies are instrumental for gaining a mechanistic understanding of cellular processes. Determining these structures is a major challenge for experimental techniques, such as X-ray crystallography, NMR spectroscopy and electron microscopy (EM). Thus, computational modeling techniques, including molecular docking, are required. The development of most molecular docking methods has so far been focused on modeling of binary complexes. We have recently introduced the MultiFit method for modeling the structure of a multisubunit complex by simultaneously optimizing the fit of the model into an EM density map of the entire complex and the shape complementarity between interacting subunits. Here, we report algorithmic advances of the MultiFit method that result in an efficient and accurate assembly of the input subunits into their density map. The successful predictions and the increasing number of complexes being characterized by EM suggests that the CAPRI challenge could be extended to include docking-based modeling of macromolecular assemblies guided by EM.

Scoring functions for cryoEM density fitting

In fitting atomic structures into cryoEM density maps of macromolecular assemblies, the cross-correlation function (CCF) is the most prevalent method of scoring the goodness-of-fit. However, there are still many possible, less studied ways of scoring fits. In this paper, we introduce four scores new to cryoEM fitting and compare their performance to three known scores. Our benchmark consists of (a) 4 protein assemblies with simulated maps at 5-20 Å resolution, including the heptameric ring of GroEL; and (b) 4 experimental maps of GroEL at ∼6-23 Å resolution with corresponding fitted atomic models. We perturb each fit 1000 times and assess each new fit with each score. The correlation between a score and the Cα RMSD of each fit from the "correctly" fitted structure shows that the CCF is one of the best scores, but in certain situations could be augmented or even replaced by other scores. For instance, our implementation of a score based on mutual information outperforms or is comparable to the CCF in almost all test cases, and our new "envelope score" works as well as the CCF at sub-nanometer resolution but is an order of magnitude faster to calculate. The results also suggest that the width of the Gaussian function used to blur the atomic structure into a density map can significantly affect the fitting process. Finally, we show that our score-testing method, when combined with the Laplacian CCF or the mutual information scores, can be used as a statistical tool for improving cryoEM density fitting.

Modeling protein structure at near atomic resolutions with Gorgon

Electron cryo-microscopy (cryo-EM) has played an increasingly important role in elucidating the structure and function of macromolecular assemblies in near native solution conditions. Typically, however, only non-atomic resolution reconstructions have been obtained for these large complexes, necessitating computational tools for integrating and extracting structural details. With recent advances in cryo-EM, maps at near-atomic resolutions have been achieved for several macromolecular assemblies from which models have been manually constructed. In this work, we describe a new interactive modeling toolkit called Gorgon targeted at intermediate to near-atomic resolution density maps (10-3.5 Å), particularly from cryo-EM. Gorgon's de novo modeling procedure couples sequence-based secondary structure prediction with feature detection and geometric modeling techniques to generate initial protein backbone models. Beyond model building, Gorgon is an extensible interactive visualization platform with a variety of computational tools for annotating a wide variety of 3D volumes. Examples from cryo-EM maps of Rotavirus and Rice Dwarf Virus are used to demonstrate its applicability to modeling protein structure.

Modeling of proteins and their assemblies with the integrative modeling platform

To understand the workings of the living cell, we need to characterize protein assemblies that constitute the cell (for example, the ribosome, 26S proteasome, and the nuclear pore complex). A reliable high-resolution structural characterization of these assemblies is frequently beyond the reach of current experimental methods, such as X-ray crystallography, NMR spectroscopy, electron microscopy, footprinting, chemical cross-linking, FRET spectroscopy, small-angle X-ray scattering, and proteomics. However, the information garnered from different methods can be combined and used to build computational models of the assembly structures that are consistent with all of the available datasets. Here, we describe a protocol for this integration, whereby the information is converted to a set of spatial restraints and a variety of optimization procedures can be used to generate models that satisfy the restraints as much as possible. These generated models can then potentially inform about the precision and accuracy of structure determination, the accuracy of the input datasets, and further data generation. We also demonstrate the Integrative Modeling Platform (IMP) software, which provides the necessary computational framework to implement this protocol, and several applications for specific-use cases.

Functional and structural studies of TRP channels heterologously expressed in budding yeast

The transient receptor potential (TRP) superfamily is one of the largest families of cation channels. The metazoan TRP family has been subdivided into major branches: TRPC, TRPA, TRPM, TRPP, TRPV, TRPML, and TRPN, while the TRPY family is found in fungi. They are involved in many physiological processes and in the pathogenesis of various disorders. An efficient high-yield expression system for TRP channels is a necessary step towards biophysical and biochemical characterization and structural analysis of these proteins, and the budding yeast, Saccharomyces cerevisiae has proven to be very useful for this purpose. In addition, genetic screens in this organism can be carried out rapidly to identify amino acid residues important for function and to generate useful mutants. Here we present an overview of current developments towards understanding TRP channel function and structure using Saccharomyces cerevisiae as an expression system. In addition, we will summarize recent progress in understanding gating mechanisms of TRP channels using endogenously expressing TRPY channels in S. cerevisiae, and insights gained from genetic screens for mutants in mammalian channels. The discussion will focus particular attention of the use of cryo-electron microscopy (cryo-EM) to determine TRP channel structure, and outlines a "divide and concur" methodology for combining high resolution structures of TRP channel domains determined by X-ray crystallography with lower resolution techniques including cryo-EM and spectroscopy.

Structural biology of TRP channels

Structural studies on TRP channels, while limited, are poised for a quickened pace and rapid expansion. As of yet, no high-resolution structure of a full length TRP channel exists, but low-resolution electron cryomicroscopy structures have been obtained for 4 TRP channels, and high-resolution NMR and X-ray crystal structures have been obtained for the cytoplasmic domains, including an atypical protein kinase domain, ankyrin repeats, coiled coil domains and a Ca(2+)-binding domain, of 6 TRP channels. These structures enhance our understanding of TRP channel assembly and regulation. Continued technical advances in structural approaches promise a bright outlook for TRP channel structural biology.

Structural bioinformatics: deriving biological insights from protein structures

Structural bioinformatics can be described as an approach that will help decipher biological insights from protein structures. As an important component of structural biology, this area promises to provide a high resolution understanding of biology by assisting comprehension and interpretation of a large amount of structural data. Biological function of protein molecules can be inferred from their three-dimensional structures by comparing structures, classifying them and transferring function from a related protein or family. It is well known now that the structure space of protein molecules is more conserved than the sequence space, making it important to seek functional associations at the structural level. An added advantage of structural bioinformatics over simpler sequence-based methods is that the former also provides ultimate insights into the mechanisms by which various biological events take place. A bird's eye-view of the different aspects of structural bioinformatics is given here along with various recent advances in the area including how knowledge obtained from structural bioinformatics can be applied in drug discovery.

Discrete structure of an RNA folding intermediate revealed by cryo-electron microscopy

RNA folding occurs via a series of transitions between metastable intermediate states. It is unknown whether folding intermediates are discrete structures folding along defined pathways or heterogeneous ensembles folding along broad landscapes. We use cryo-electron microscopy and single-particle image reconstruction to determine the structure of the major folding intermediate of the specificity domain of a ribonuclease P ribozyme. Our results support the existence of a discrete conformation for this folding intermediate.